• 제목/요약/키워드: Lyapunov Theory

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리아프노프 함수를 이용한 풍력 발전기 비선형 피치 및 토크 제어기 설계 (Nonlinear Pitch and Torque Controller Design for Wind Turbine Generator Using Lyapunov Function)

  • 김국선;노태수;전경언;김지언
    • 대한기계학회논문집A
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    • 제36권10호
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    • pp.1147-1154
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    • 2012
  • 본 논문에서는 풍력발전기의 회전속도와 출력을 제어하기 위한 블레이드 피치 제어기 및 발전기 토크 제어 기법을 제시하고 비선형 시뮬레이션을 통하여 그 성능을 확인하였다. 회전속도 오차 및 출력오차를 이용한 양한정 함수를 정의하고 리아프노프 안정성 이론을 적용하여 정적 피치 제어기와 동적 토크 제어기를 설계하고, 제어기 설계 모델과 실제 적용 모델간의 차이를 보상할 수 있도록 시뮬레이션 기반 최적화를 이용하여 설계 인자 값을 결정하였다. 풍력발전기 제어기 설계에 가장 많이 사용되는 동력 전달계 모델을 기반으로 제어기 설계 절차를 예시하였고, 대표적으로 사용되는 비례-적분-미분 제어 및 최대 출력점 추종 토크 제어기와 성능 비교를 통하여 제안된 제어 설계 기법의 타당성을 검증하였다.

백스테핑기법과 신경회로망을 이용한 적응 재형상 비행제어법칙 (Reconfigurable Flight Control Law Using Adaptive Neural Networks and Backstepping Technique)

  • 신동호;김유단
    • 제어로봇시스템학회논문지
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    • 제9권4호
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    • pp.329-339
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    • 2003
  • A neural network based adaptive controller design method is proposed for reconfigurable flight control systems in the presence of variations in aerodynamic coefficients or control effectiveness decrease caused by control surface damage. The neural network based adaptive nonlinear controller is developed by making use of the backstepping technique for command following of the angle of attack, sideslip angle, and bank angle. On-line teaming neural networks are implemented to guarantee reconfigurability and robustness to the uncertainties caused by aerodynamic coefficients variations. The main feature of the proposed controller is that the adaptive controller is designed with assumption that not any of the nonlinear functions of the system is known accurately, whereas most of the previous works assume that only some of the nonlinear functions are unknown. Neural networks loam through the weight update rules that are derived from the Lyapunov control theory. The closed-loop stability of the error states is also investigated according to the Lyapunov theory. A nonlinear dynamic model of an F-16 aircraft is used to demonstrate the effectiveness of the proposed control law.

Stability Analysis for the Deployment of Unmanned Surface Vehicles

  • Dharne, Avinash G.;Lee, Jaeyong
    • Journal of Advanced Marine Engineering and Technology
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    • 제39권2호
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    • pp.159-165
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    • 2015
  • Motion control schemes are generally classified into three categories (point stabilization, trajectory tracking, and path following). This paper deals with the problem which is associated with the initial deployment of a group of Unmanned Surface Vehicle (USVs) and corresponding point stabilization. To keep the formation of a group of USVs, it is necessary to set the relationship between each vehicle. A forcing functions such as potential fields are designed to keep the formation and a graph Laplacian is used to represent the connectivity between vehicle. In case of fixed topology of the graph representing the communication between the vehicles, the graph Laplacian is assumed constant. However the graph topologies are allowed to change as the vehicles move, and the system dynamics become discontinuous in nature because the graph Laplacian changes as time passes. To check the stability in the stage of deployment, the system is modeled with Kronecker algebra notation. Filippov's calculus of differential equations with discontinuous right hand sides is then used to formally characterize the behavior of USVs. The stability of the system is analyzed with Lyapunov's stability theory and LaSalle's invariance principle, and the validity is shown by checking the variation of state norm.

DSP(TMS320C50) 칩을 사용한 산업용 로봇의 적응-신경제어기의 실현 (Implementation of the Adaptive-Neuro Controller of Industrial Robot Using DSP(TMS320C50) Chip)

  • 김용태;정동연;한성현
    • 한국공작기계학회논문집
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    • 제10권2호
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    • pp.38-47
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    • 2001
  • In this paper, a new scheme of adaptive-neuro control system is presented to implement real-time control of robot manipulator using Digital Signal Processors. Digital signal processors, DSPs, are micro-processors that are particularly developed for fast numerical computations involving sums and products of measured variables, thus it can be programmed and executed through DSPs. In addition, DSPs are as fast in computation as most 32-bit micro-processors and yet at a fraction of therir prices. These features make DSPs a viable computational tool in digital implementation of sophisticated controllers. Unlike the well-established theory for the adaptive control of linear systems, there exists relatively little general theory for the adaptive control of nonlinear systems. Adaptive control technique is essential for providing a stable and robust perfor-mance for application of robot control. The proposed neuro control algorithm is one of learning a model based error back-propagation scheme using Lyapunov stability analysis method.The proposed adaptive-neuro control scheme is illustrated to be a efficient control scheme for the implementation of real-time control of robot system by the simulation and experi-ment.

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미지의 불확실한 시스템에 대한 강인한 적응 제어 (Robust adaptive control for unknown uncertain systems)

  • 김진환;이정휴;정사철;함철주;함운철
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 1992년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 19-21 Oct. 1992
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    • pp.760-765
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    • 1992
  • 본 논문에서는 미지의 불확실한 시스템에 적용할 수 있는 제어 알고리즘을 제안하였다. n차 수 단일 입출력 시스템의 상태를 "uncontrolled" 상태와 "controlled" 상태로 분리시키며 아울러 uncontrolled 부시스템이 임의의 n-1개의 특성근(eigen values)을 갖도록 하는 변환 행렬을 유도하고, 이를 이용하여 새로운 강인한 제어기를 설계하였다. 적응 제어 이론과 가변 구조 제어 이론의 개념을 도입하여 새로운 제어 법칙을 제안하였으며 제안된 제어기의 안정도는 Lyapunov 안정도 이론을 이용하여 증명하였다. 컴퓨터 시뮬레이션 결과 제안된 적응 제어 알고리즘이 강인성과 안정성을 갖음을 확인할 수 있었다.

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Preliminary Test of Adaptive Neuro-Fuzzy Inference System Controller for Spacecraft Attitude Control

  • Kim, Sung-Woo;Park, Sang-Young;Park, Chan-Deok
    • Journal of Astronomy and Space Sciences
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    • 제29권4호
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    • pp.389-395
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    • 2012
  • The problem of spacecraft attitude control is solved using an adaptive neuro-fuzzy inference system (ANFIS). An ANFIS produces a control signal for one of the three axes of a spacecraft's body frame, so in total three ANFISs are constructed for 3-axis attitude control. The fuzzy inference system of the ANFIS is initialized using a subtractive clustering method. The ANFIS is trained by a hybrid learning algorithm using the data obtained from attitude control simulations using state-dependent Riccati equation controller. The training data set for each axis is composed of state errors for 3 axes (roll, pitch, and yaw) and a control signal for one of the 3 axes. The stability region of the ANFIS controller is estimated numerically based on Lyapunov stability theory using a numerical method to calculate Jacobian matrix. To measure the performance of the ANFIS controller, root mean square error and correlation factor are used as performance indicators. The performance is tested on two ANFIS controllers trained in different conditions. The test results show that the performance indicators are proper in the sense that the ANFIS controller with the larger stability region provides better performance according to the performance indicators.

Trajectory tracking control of underactuated USV based on modified backstepping approach

  • Dong, Zaopeng;Wan, Lei;Li, Yueming;Liu, Tao;Zhang, Guocheng
    • International Journal of Naval Architecture and Ocean Engineering
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    • 제7권5호
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    • pp.817-832
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    • 2015
  • This paper presents a state feedback based backstepping control algorithm to address the trajectory tracking problem of an underactuated Unmanned Surface Vessel (USV) in the horizontal plane. A nonlinear three Degree of Freedom (DOF) underactuated dynamic model for USV is considered, and trajectory tracking controller that can track both curve trajectory and straight line trajectory with high accuracy is designed as the well known Persistent Exciting (PE) conditions of yaw velocity is completely relaxed in our study. The proposed controller has further been enriched by incorporating an integral action additionally for enhancing the steady state performance and control precision of the USV trajectory tracking control system. Global stability of the overall system is proved by Lyapunov theory and Barbalat's Lemma, and then simulation experiments are carried out to demonstrate the effectiveness of the controller designed.

카오스 이론을 적용한 보행분석 연구 (Application of the Chaos Theory to Gait Analysis)

  • 박기봉;고재훈;문병영;서정탁;손권
    • 대한기계학회논문집A
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    • 제30권2호
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    • pp.194-201
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    • 2006
  • Gait analysis is essential to identify accurate cause and knee condition from patients who display abnormal walking. Traditional linear tools can, however, mask the true structure of motor variability, since biomechanical data from a few strides during the gait have limitation to understanding the system. Therefore, it is necessary to propose a more precise dynamic method. The chaos analysis, a nonlinear technique, focuses on understand how variations in the gait pattern change over time. Eight healthy eight subjects walked on a treadmill for 100 seconds at 60 Hz. Three dimensional walking kinematic data were obtained using two cameras and KWON3D motion analyzer. The largest Lyapunov exponent from the measured knee angular displacement time series was calculated to quantify local stability. This study quantified the variability present in time series generated from gait parameter via chaos analysis. Knee flexion-extension patterns were found to be chaotic. The proposed Lyapunov exponent can be used in rehabilitation and diagnosis of recoverable patients.

크기 및 변화율 제한을 갖는 비선형 시스템의 제어 (Nonlinear Control with Magnitude and Rate Constraints)

  • 이정국;이금원;이준모
    • 융합신호처리학회논문지
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    • 제8권2호
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    • pp.130-135
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    • 2007
  • 본 논문에서는 다항식형태의 비선형성을 갖는 미지의 파라미터를 갖는 2차원의 공탄성(aeroelastic) 시스템에 대한 제어기 설계를 다룬다. 특히 제어기구현에 사용되는 상태 및 actuator 구동기신호가 크기, 변화율 및 대역제약조건을 가지는 경우는 실현이 불가능한데, 이 경우에도 각각에 대한 필터를 사용하여 해결한다. 우선 backstepping에 기초한 오차신호를 정의하고, 명령신호 및 필터출력 신호에 대한 추적오차신호를 정의하며, 필터구성에 따른 보상된 추적오차신호를 재정의한다. 안정화를 위하여 Lyapunov함수를 도입하고, 안정성 원리에 따라 적응식을 유도한다. 시뮬레이션을 통해서 유용성을 입증한다.

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에너지소산 제어 알고리듬의 제어이득 산정 (Control-Gain Estimation of Energy Dissipation Control Algorithms)

  • 이상현;강상훈;민경원
    • 한국전산구조공학회논문집
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    • 제17권4호
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    • pp.343-350
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    • 2004
  • 본 논문은 에너지소산 제어알고리듬의 제어이득 산정에 관하여 연구하였다. Lyapunov안정성이론에 기초하여 속도 되먹임 포화제어알고리듬, 뱅뱅제어 알고리듬 그리고 에너지게인 제어알고리듬을 제안하였고, 이 알고리듬의 성능을 평가하고 비교하였다. 속도 되먹임 포화제어알고리듬과 에너지게인 제어알고리듬에서는 포화현상을 고려하였고, 뱅뱅제어에서는 경계층을 이용하여 채터링현상을 고려하였다. 수치적인 해석을 통해서 제안된 제어알고리듬이 바람하중에 의해 야기되어지는 구조물의 에너지를 효과적으로 소산시킬 수 있음을 보여주었다.